The presidential campaign now moves here to Pennsylvania and four other Eastern states, with the two front-runners lengthening their leads over challengers whose White House prospects seem to be dimming by the day.

But the twin victories Tuesday night in New York illuminated the weaknesses as much as the strengths of Donald J. Trump and Hillary Rodham Clinton.

Both Mr. Trump, who bases his casino-and-real-estate empire in New York, and Ms. Clinton, who was elected to the Senate twice from the Empire State, cruised to decisive victories Tuesday — but exit polls showed deep unease among Republicans about the prospect of a Trump nomination and showed serious skepticism among young voters about a Clinton general-election campaign.

Even as Mr. Trump and Ms. Clinton surged ahead in the delegate chase — leaving their rivals with near-impossible prospects of surpassing them — the two face the likelihood of emerging from the bruising caucus and primary season with dangerously divided parties and with certain natural constituencies exceedingly wary about the nominees the two parties are likely to send into the November election.

Meanwhile, important dramas are unfolding within each party, raising vital questions about the course of the campaign in the weeks before the Cleveland and Philadelphia conventions.

For the Republicans, the question is whether a candidate who has triumphed by breaking all the political rules can be denied the party’s nomination because of wrinkles in the party rules. Those rules require 1,237 delegates to capture the nomination. “We’re leading by a lot and can’t be caught,” Mr. Trump said Tuesday night, and hardly anyone can contest that. But the question remains whether a decisive lead short of the majority that the rules require is sufficient to win the nomination.

Mr. Trump may be making an appealing but flawed case when he argues, as he did in his victory speech Tuesday, that “it’s a crooked system, it’s a system that’s rigged.” The rules were established long before Mr. Trump contemplated a presidential campaign and they apply equally to Mr. Trump, to Sen. Ted Cruz of Texas and to Gov. John Kasich of Ohio and, for that matter, to former Gov. Jeb Bush of Florida, who left the race long ago.

The latest Wall Street Journal/?NBC News poll showed that three out of five Republicans believe the nomination should go to the candidate with the most votes in the primary. But the issue is whether party leaders rule that rules are rules — and whether Mr. Cruz’s stealth effort at obscure state party proceedings to sway delegates to his cause prevents Mr. Trump from winning a first-ballot victory.

In the Democratic Party, Ms. Clinton brought to an abrupt end the momentum Sen. Bernie Sanders of Vermont built up earlier this month — and her strong victory in the state where her rival was born is raising new questions about the relevance of his candidacy.

The Sanders campaign began as a quixotic crusade against climate change, big money in politics and the wealth gap, then transformed into a legitimate alternative to the former secretary of state. It now seems once again to be taking on the cloak of symbolism rather than realism.

In the coming days, Mr. Sanders will face hard questions about the rationale for his campaign and challenges about whether his candidacy, which took on an increasingly shrill tone in New York, may be hurting the Democrats’ prospects in the general election. This was especially apparent Tuesday night, when Ms. Clinton said of Mr. Sanders’ supporters: “There is much more that unites us than divides us.”

In her fortnight in the cauldron of New York politics as well as in her Manhattan victory celebration, Ms. Clinton continued her pivot toward November, saying that hers was the only candidacy this year to capture 10 million votes. That echoed Mr. Trump’s triumphal declaration that he has brought millions of new voters into Republican primary contests. The two front-runners appear to be campaigning against fading rivals, and increasingly they are shoving those rivals into the past rhetorically.

But the two front-runners still have major challenges ahead.

Both have astonishing negative ratings among voters — 65 percent for Mr. Trump and 56 percent for Ms. Clinton, according to the latest Wall Street Journal/?NBC News Poll. About half of voters said they would be scared if Mr. Trump were elected, according to a New York Times/?CBS News Poll late last month.

Exit polls from New York showed that 60 percent of Republicans who voted in the state’s primary believe the GOP campaign has divided the party — and more than a quarter saying they voted not for a candidate but against another candidate. About two out of five Republicans indicated they were troubled by the prospect of a Trump presidency, with about a quarter saying they wouldn’t vote for Mr. Trump.

As for Ms. Clinton, she carried only a fifth of Democratic voters aged 18 to 24. Political professionals often play down the impact of the youth vote; the percentage of young people who cast ballots customarily is relatively low. Yet Democratic analysts were astonished at the tide of young people who supported Barack Obama in 2008 and theorized that they would be the basis of a decade of Democratic dominance.

In 2016, if Ms. Clinton cannot corral those young voters into the Democratic coalition, she could relinquish a natural advantage her party won eight years ago.

Even so, the campaign is moving into friendly territory for both front-runners.

Ms. Clinton defeated Barack Obama in Pennsylvania eight years ago, and her husband carried the state both in 1992 and in 1996. She holds a 13 percent lead over Mr. Sanders in the Real Clear Politics survey average here.

Mr. Trump’s Pennsylvania lead is more than 20 points. Both front-runners are well positioned in Delaware and Maryland, which also vote next Tuesday.

Mr. Kasich harbors hopes in Connecticut and Mr. Sanders has high hopes for Rhode Island, but neither state has the delegate power to change the political narrative.

All that said, faint glimmers of hope remain for those left behind in New York. Mr. Trump’s team still has not mastered the organizational skills required to win a contested convention. And national polls still show Mr. Sanders within striking distance of Ms. Clinton. Who would have guessed?

David Shribman, a Pulitzer Prize winner in journalism, is executive editor of the Pittsburgh Post-Gazette.